6 T. unsalted butter, cut into ½ inch pieces, at room temperature
1¼ c. all-purpose flour
½ t. sugar
1 large egg, lightly beaten
1 butternut squash (1¾ lbs.), peeled and sliced into ¼-inch thick half moons
2 T. unsalted butter, melted
2 t. finely chopped fresh sage
3 T. honey
¼ c. grated Parmesan
¼ c. plain breadcrumbs
1½ c. Gruyere cheese, cut into small cubes
2 t. white wine vinegar
½ t. crushed red pepper
For the crust:
Butter a 9-inch springform pan. Put the flour, sugar, and ½ t. salt in a food processor and pulse to combine. Add the butter and process until thoroughly combined with no visible chunks. Add the egg and pulse until the dough just starts to clump. Transfer the dough to the springform pan and press it evenly on the bottom and one inch up the sides. Refrigerate for 30 minutes.
For the filling:
Adjust oven rack to middle position and preheat the oven to 375° F.
Toss the butternut squash slices with the melted butter, sage, 1 T. honey, and 1 t. salt in a large bowl. Sprinkle the Parmesan and breadcrumbs evenly on the bottom of the crust, then scatter over ½ cup of the Gruyere cubes. Lay out a single layer of butternut squash slices, breaking off pieces of squash to fill any gaps. Scatter another ½ cup of Gruyere over the squash. Top with the rest of the butternut squash slices and the remaining Gruyere.
Put the springform pan on a baking sheet and bake until the squash can be pierced easily with a knife, about 1 hour and 40 minutes to 1 hour 50 minutes. (If crust gets too dark, cover loosely with foil.)
Meanwhile, combine the vinegar, crushed red pepper, and the remaining 2 T. honey in a microwave-safe bowl large enough to contain it (the honey may boil over in the microwave). Microwave for 30 seconds. Reserve.
When tart comes out of the oven, drizzle all over with the spicy liquid and serve immediately.